Catadioptric imaging systems for digital scanner

ABSTRACT

Projection optical system for forming an image on a substrate and including an illumination relay lens and a projection lens each of which is a catadioptric system. The projection lens may include two portions in optical communication with one another, the first of which is dioptric and the second of which is catadioptric. In a specific case, the projection optical system satisfies 
               4   &lt;            β   I                 β   T            &lt;   30     ,         
where β I  and β T  are magnifications of the first portion and the overall projection lens. Optionally, the projection lens may be structured to additionally satisfy
 
               6   &lt;            β   II                 β   T            &lt;   20     ,         
where β II  is a magnification of the second portion. A digital scanner including such projection optical system and operating with UV light having a spectral bandwidth on the order of 1 picometer. Method for forming an image with such projection optical system.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional from U.S. patent application Ser. No. 14/559,684 now published as U.S. 2015/0146185, which is a continuation-in-part from the U.S. patent application Ser. No. 14/550,465 and now granted as U.S. Pat. No. 9,638,906, which in turn claims benefit of and priority from the U.S. Provisional Patent Application No. 61/907,747. The disclosure of each of the above-identified provisional application is incorporated herein by reference.

TECHNICAL FIELD

The present invention relates generally to lithographic projection optics such as that, which may be used to form an image of a reticle on a semiconductor wafer used in semiconductor manufacturing and, in particular, to lithographic projection optics that are designed to operate with numerical aperture equal to or exceeding 1.0.

BACKGROUND

Chromatic aberrations of optical projection systems that utilize refractive optical elements understandably depend on the bandwidth of light used for projecting an image of a chosen object and, depending on the severity of such aberrations, may require complex designs for aberration compensation. It may be necessary to correct chromatic aberrations for broader bandwidth of light depending on the type of light source.

Attempts were made to address the loss-of-image-contrast problem by devising such projection systems that employ an SLM and that are built around the use of a projection optics containing a catadioptric sub-portion. The proposed optical projection systems can be viewed as including two main portions or sub-systems: a first portion structured as an illumination relay configured to deliver light from a light source to the SLM and to perform what in the art is referred to as “field framing”, and a second portion configured to project the light distribution from the plane of the SLM onto the image plane (the wafer) and referred to as a projection sub-system. While a projection sub-system was proposed to be structured as a catadioptric system, the illumination relay is kept conventionally dioptric (which causes, notably, an overall optical projection system to be sometimes impractically long, unless the optical path is intentionally folded with plane mirrors). It is recognized that the existing solutions still require improvements with respect to several operationally important aspects.

Accordingly, at least the greater-than-acceptable levels of chromatic aberrations in existing projection systems and insufficient reduction ratios define a need in redesign of an optical projection system for efficient use in conjunction with a digital scanner.

SUMMARY

Embodiments of the invention provide a projection optical system configured to form an image on a substrate and including a catadioptric illumination relay lens and a catadioptric projection lens. A projection optical system may include a spatial light modulator (SLM) positioned to receive light from the catadioptric illumination relay lens and reflect said light towards the catadioptric projection lens.

Embodiments additionally provide a projection optical system for forming an image on an image plane, which system contains a catadioptric projection lens that includes first and second portions in optical communication with one another; the second portion is configured as a catadioptric optical system designed to form an intermediate optical image at a location between the elements of the second portion; the first portion is configured as a dioptric optical system disposed to transfer light from the location of the intermediate optical image to the image plane of the projection optical system to form the image at the image plane. The catadioptric projection lens is structured to satisfy an operational condition of

${4 < \frac{\beta_{I}}{\beta_{T}} < 30},$ wherein β_(I) denotes a magnification of the first portion and β_(T) denotes a magnification of the catadioptric projection lens.

Embodiments of the invention additionally provide a projection optical system for forming an image on an image plane. Such system includes a catadioptric projection lens that contains first and second portions in optical communication with one another, where the second portion is designed as a catadioptric optical system configured to form an intermediate optical image at a location between the elements of the second portion. At the same time, the first portion is designed as a dioptric optical system and is disposed such as to transfer light from the location of the intermediate image to the image plane of the projection optical system. The catadioptric projection lens is configured to satisfy an operational condition of

${6 < \frac{\beta_{II}}{\beta_{T}} < 20},$ wherein β_(II) denotes a magnification of the second portion and β_(T) denotes a magnification of the catadioptric projection lens.

Yet another embodiment provides a projection optical system for forming an image on an image plane and including a catadioptric projection lens the first and second portions of which are in optical communication with one another. Here, the second portion is configured as a catadioptric optical system that includes first and second negative lenses and a concave mirror to form an intermediate optical image at a location between the elements of the second portion, while the first portion is configured as a dioptric optical system disposed to form an image of the intermediate optical image at the image plane. The first negative lens has concave and convex surfaces, the concave surface of the first negative lens facing away from the concave mirror. A concave surface of the second negative lens is immediately adjacent to the concave mirror.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more fully understood by referring to the following Detailed Description in conjunction with the generally not-to-scale schematic Drawings, of which:

FIG. 1A is a diagram illustrating a conventionally-structured optical imaging system delivering light from a filed framing plane through an SLM and containing an 0.5× dioptric illuminator relay and a 50× catadioptric projection lens;

FIG. 1B is a diagram illustrating a first portion of the catadioptric projection lens of the embodiment of FIG. 1A;

FIG. 1C is a diagram illustrating a second portion of the catadioptric projection lens of the embodiment of FIG. 1A;

FIG. 1D is a diagram providing details of the dioptric illuminator relay of the embodiment of FIG. 1A;

FIG. 2A is a diagram of an optical imaging system according to an embodiment of the invention structured to deliver light from a filed framing plane through an SLM and containing the same 50× catadioptric projection lens as the embodiment of FIG. 1A but in which the illuminator relay is structured as a 0.5× catadioptric sub-system;

FIG. 2B is a diagram providing details of the catadioptric illuminator relay of the embodiment of FIG. 2A;

FIG. 3A is a diagram illustrating a conventionally-structured optical imaging system delivering light from a filed framing plane through an SLM and containing an 0.5× dioptric illuminator relay and a 200× catadioptric projection lens;

FIG. 3B is a diagram illustrating the catadioptric projection lens of the embodiment of FIG. 3A;

FIG. 3C is a diagram providing details of the dioptric illuminator relay of the embodiment of FIG. 3A;

FIG. 4 is a diagram of an optical imaging system according to an embodiment of the invention structured to deliver light from a filed framing plane through an SLM and containing the same 200× catadioptric projection lens as the embodiment of FIG. 3A but in which the illuminator relay is structured as a 0.5× catadioptric sub-system;

FIG. 5A shows plots representing ray aberrations, within a defined spectral bandwidth around the operating wavelength, at a plane of the SLM (element 24) of the embodiment of FIG. 1A;

FIG. 5B shows plots representing ray aberrations, within a defined spectral bandwidth around the operating wavelength, in the image plane (wafer) of the embodiment of FIG. 1A;

FIG. 6 shows plots representing ray aberrations, within a defined spectral bandwidth around the operating wavelength, in the image plane (wafer) of the embodiment of FIG. 2A;

FIG. 7A shows plots representing ray aberrations, within a defined spectral bandwidth around the operating wavelength, at a plane of the SLM (element 24) of the embodiment of FIG. 3A;

FIG. 7B shows plots representing ray aberrations, within a defined spectral bandwidth around the operating wavelength, in the image plane (wafer) of the embodiment of FIG. 3A;

FIG. 8 shows plots representing ray aberrations, within a defined spectral bandwidth around the operating wavelength, in the image plane (wafer) of the embodiment of FIG. 4;

FIG. 9 is a schematic diagram illustrating a concept of an exposure device (digital scanner) utilizing an embodiment of the invention.

FIG. 10 is a flow-chart illustrating a method for forming an optical image with an embodiment of the projection optical system.

DETAILED DESCRIPTION

Embodiments of the invention provide a projection optical system for forming an image on a substrate and including a catadioptric illumination relay lens and a catadioptric projection lens. A projection optical system may include a spatial light modulator (SLM) positioned to receive light from the catadioptric illumination relay lens and reflect said light towards the catadioptric projection lens. The numerical aperture of the projection optical system is equal to or exceeds 1.0, while the image is formed with a size reduction ratio of at least 50×. When structured to operate at such reduction ratio and in UV light having a central wavelength of about 193.3 nm and a spectral bandwidth of about 1 picometer, the operation of the projection system is characterized by a first Strehl ratio at the central wavelength and a second Strehl ratio across the spectral bandwidth, both of which exceed 0.95. When structured to operate at a reduction ratio of 200× and in the same UV light, both the first and second Strehl ratios exceed 0.98. Embodiments also provide a digital scanner comprising such projection optical system.

Embodiments of the present invention provide a solution for the lack of a hyper-NA (i.e., with NA values exceeding 1.0 and equal to, for example, 1.35) high reduction ratio (50× to 200×, for example) optical projection system configured for efficient use with a digital scanner, which system is operable, for practical lithographic purposes, across a spectral bandwidth of light on the order or 1 pm without substantial loss of image contrast caused by chromatic aberrations. Embodiments include optical projection systems in which both the illumination relay sub-portion and the projection sub-portion are catadioptric.

While one can attempt to argue that the precise and accurate performance of the projection sub-system (i.e., a sub-system of the overall projection system that re-images light from the SLM onto the wafer) may be more critical than that of the illumination relay sub-system because the actual semiconductor circuit structure is produced by reimaging the SLM onto the wafer, the design data discussed below prove that continued utilization of a conventionally dioptrically-designed illumination relay sub-system leads to substantial underperformance of the overall projection system.

Specifically, a comparison of operational characteristics of (i) a conventional projection system including a 0.5× dioptric illumination relay subsystem (interchangeably referred to herein as an “illuminator relay”) and a 50× catadioptric projection sub-system (interchangeably referred to herein as a “catadioptric projection lens”) and those of (ii) an embodiment of the present invention including a 0.5× catadioptric illuminator relay and a 50× catadioptric projection lens is provided. Also are analyzed (and compared with one another) operational characteristics of (iii) a conventionally-designed system combining a 0.5× dioptric illuminator relay with a 200× catadioptric projection lens and those of (iv) an embodiment of the invention combining the 0.5× dioptric illuminator relay with a 200× catadioptric projection lens.

Several additional notes are in order for ease of understanding of the following disclosure. Tables 1 through 4 in the following discussion summarize the prescriptions for designs of various optical systems and their subsystems that were performed with Code V and that are discussed in reference to corresponding Figures. In these Tables, optical elements are numbered in a “backward” fashion, starting with the semiconductor wafer (defining the image plane) towards the source of light, which makes it easier, as would be appreciated by a skilled artisan, to define the NA and telecentricity in wafer space during the process of optical design. The semiconductor wafer (with a wafer plane labeled as 1 in the Tables) is submerged in fluid (for example, water, as shown in inset of FIG. 1B) that separates the closest lens (marked as element 2 in the Tables) from it. This condition applies to each of the presented embodiments. Positive radius value indicates that the center of curvature is to the right, while a negative radius value indicates that the center of curvature is to the left; dimensions are provided in millimeters; thickness is defined as an axial distance to the next surface; and an indicated image diameter is a paraxial value and not a ray traced value. Furthermore, with respect to decentering constants, a decenter defines a new coordinate system (displaced and/or rotated) in which subsequent surfaces are defined. Surfaces following a decenter are aligned on the local mechanical axis (z-axis) of the new coordinate system. The new mechanical axis remains in use for referencing purposes until expressly changed by another decenter. The order in which displacements and tilts are applied to a given surface is specified using different decenter types and these generate different new coordinate systems; those used in this disclosure are explained below. Alpha, beta, and gamma values are presented in degrees. Additionally, with respect to chromatic aberrations, a reduction in Strehl ratio between monochromatic and polychromatic deigns represents the contrast loss from chromatic aberrations over the specified spectral band, while a variation in best individual focus shows the residual field curvature.

An embodiment of the catadioptric optical projection system according to the invention is designed to ensure, in operation, at least a 50× reduction ratio and is characterized by a hyper-NA (of at least 1.0) catadioptric projection lens and an instantaneous line field of view (one dimensional, ID, FOV) of about 3.6 mm on the surface of the wafer. The projection optical system is structured to be compatible with principles of maskless lithography, according to which the conventionally used mask (or reticle) is replaced by an SLM. The SLM may take a form of a ID array of microelectromechanical actuators, or MEMS, for example, or actuators on the scale of a few tens or hundreds of nanometers (NEMS). U.S. Pat. Nos. 5,312,513; 5,523,193; 7,110,082; 7,206,117; 7,952,780; and 2013/0003166, the disclosure of each of which is incorporated by reference herein, provide additional information on SLM technology.

Example 1: Catadioptric Embodiment with a 50× Reduction Ratio

FIGS. 1A, 1B, 1C, and 1D illustrate an optical imaging system 100 providing a 50× reduction ratio and structured conventionally in that, while the projection lens portion (I and II) includes a catadioptric optical system, the illumination relay portion (III) is dioptric. To illustrate contradistinctively advantageous operational characteristics of a fully-catadioptric system configured according to an embodiment of the present invention, a comparison is made with a 50×-reducing optical system of FIGS. 2A and 2B, in which each of the projection lens portion (I and II) and the illuminator relay (III-CAT) is structured as a catadioptric system. For the purposes of comparison, the projection lens portions of both the system of FIG. 1A and the embodiment of FIG. 2A are identical.

As shown in FIG. 1A, the illumination relay III images a field framing plane (element 33 that is illuminated with a telecentric system, not shown) onto the plane of the SLM (element 24) with a 2× magnification. The light-beam 110 further passes, upon reflection from the SLM (element 24), without obscuration into the catadioptric projection sub-system (II and I) that reduced the image on the surface of the wafer (element 1) by 50×. FIGS. 1B, 1C, and 1D show the details of sub-portions of the embodiment 100.

As shown in FIG. 2A, the embodiment 200 of the present invention includes the catadioptric projection sub-system (the combination of II and I) that is the same as in the embodiment 100, operably concatenated with the catadioptric illumination relay (III-CAT). The catadioptric illumination relay III-CAT images a field framing plane (element 34 that is illuminated with a telecentric system, not shown) onto the plane of the SLM (element 24) with a 2× magnification. The light-beam 210 further passes, upon reflection from the SLM (element 24), without obscuration into the catadioptric projection sub-system (II and I) that reduced the image on the surface of the wafer (element 1) by 50×. The resulting size of the rectangular image on the wafer surface is about 3.6×0.16 mm², which corresponds to about 180×8 mm² light distribution at the plane of the SLM and to about 90×4 mm² at the field framing plane (element 34). Optionally, blades may be utilized in the field framing plane to define sharply and/or further limit the size of the field. FIG. 2B shows the details of the optical train of the catadioptric illuminator relay III-CAT.

In both embodiments 100 and 200 (FIGS. 1A and 2A, respectively), the long dimension of the field is extended perpendicularly to the plane of the drawing (or parallel to the x-axis, as indicated). In both embodiments 100 and 200, the SLM (element 24) contains a ID array of microreflectors that is perpendicular to the plane of the corresponding drawings and is slightly more than 180 mm in length. In both embodiments the SLM is illuminated through the corresponding illumination relay (III, III-CAT) with light delivered from a high-repetition (˜1 MHz) UV laser source having a specified spectral bandwidth around the central wavelength of about 193 nm. The laser source used for SLM-utilizing projection optical system of the invention has a bandwidth that is about 30-fold that of a typical UV excimer laser (employed with a conventional scanner used in lithography), and has a repetition rate exceeding that of the excimer laser by about three orders of magnitude. The detailed Code V description of the optical train of the embodiment 100 is presented in Table 1A, while the corresponding description of the optical train of the embodiment of the invention 200 is presented in Table 2A.

In comparison with the design of the illumination relay III of the embodiment of FIG. 1A, and as detailed in Table 2A, the catadioptric illumination relay III-CAT includes a spherical mirror (element 29). The catadioptric projection lens (I, II) of either embodiment 100 or 200 also comprises a spherical mirror and a fold mirror (elements 14, 18), but in addition forms an intermediate image close to the fold mirror (element 14) and a number of aspheric lens elements (such as, for example, elements 13, 15, 17) that, in conjunction with the relay III-CAT, facilitate hyper-NA of 1.35 at the immersed in water wafer surface.

Descriptions of aberrations characterizing imaging through the catadioptric lens I, II of the embodiment 100 of the field framing plane 33 of the embodiment 100 of FIG. 1A onto the surface of the wafer 1 are presented in FIG. 5A and Tables 1B, 1C. Table 1B addresses the ray aberrations at the plane of the SLM (at wavelengths in an approximately 3 pm-wide spectral bandwidth centered at about 193.3 nm), and wavefront aberrations associated with the imaging through the catadioptric lens I, II of the embodiment 100). Table 1C addresses the wavefront aberrations associated with the imaging through the overall optical system of the embodiment 100, between the field framing plane 33 of the embodiment 100 and the surface of the wafer 1. FIG. 5B complements the data of FIG. 1A by providing lots of ray aberrations defined, for the embodiment of FIG. 1A, in the image plane (wafer) within a defined spectral bandwidth around the operating wavelengths. Descriptions of aberrations characterizing imaging through the overall optical system of the embodiment 200 of the invention, between the field framing plane 34 of the embodiment 200 and the surface of the wafer 1 of FIG. 2A, are summarized in FIG. 6 and Table 2B (addressing the ray aberrations and wavefront aberrations, respectively). The direct comparison between the data on aberrations for the fully-catadioptric projection lens according to the idea of the invention with those for a conventional lens highlights the advantages of the embodiment of the invention, as would be recognized by a skilled artisan.

A person of skill in the art will readily appreciate, from the data of Tables 2B and 1C, for example, that the field curvature of the fully-catadioptric design of the invention (shown in a column representing the focus position as a function of field height) is substantially smaller than that of a conventionally-design system 100. Moreover, the difference between the figures of merits describing the polychromatic aberrations and those describing monochromatic aberrations is substantially smaller for the embodiment 200 of the invention as compared to the embodiment 100. Furthermore, the values of Strehl ratio across the field for the embodiment 200 of the invention are substantially higher than those for the embodiment 100 (see, for example. Strehl ratios respectively characterizing monochromatic rms wavefront aberrations). The embodiment of the invention ensures, in addition to operationally negligible distortion of imaging between the SLM and the wafer, very small residual monochromatic aberrations on the order of about 5 milliwaves rms or less.

Example 2: Catadioptric Embodiment with 200× Reduction Ratio

FIGS. 3A, 3B, 3C illustrate an optical imaging system 300 providing a 200× reduction ratio and structured conventionally in that, while the projection lens portion (A) includes a catadioptric optical system, the illumination relay portion (B) is conventionally dioptric. To illustrate contradistinctively advantageous operational characteristics of a fully-catadioptric system according to an embodiment of the present invention, a comparison is made with a 200×-reducing optical system of FIG. 4, in which both the projection lens portion (A) and the illuminator relay (B-CAT) are structured as catadioptric systems. For the purposes of the comparison, the projection lens portions of both the system of FIG. 3A and the embodiment of FIG. 4 are identical. FIGS. 3B and 3C show the details of sub-portions of the embodiment 300.

As shown in FIG. 4, the embodiment 400 of the present invention includes the catadioptric 200×-reduction projection sub-system (A) that is the same as that of the embodiment 300, concatenated with the catadioptric illumination relay B-CAT that images a field framing plane (element 33, illuminated with a telecentric system, not shown) onto the plane of the SLM (element 24) with a 2× magnification. The resulting size of the rectangular image on the wafer surface (1) is about 0.64×0.16 mm², which corresponds to about 128×32 mm² light distribution at the plane of the SLM and to about 64×16 mm² at the field framing plane (element 33). Optionally, blades may be utilized in the field framing plane to define sharply and/or further limit the size of the field. FIG. 2B shows the details of the optical train of the catadioptric illuminator relay III-CAT. In both embodiments 300 and 300 (FIGS. 1A and 2A, respectively), the long dimension of the field is perpendicular to the plane of the drawing (or parallel to the x-axis, as indicated). The parameters of illuminating UV light used to design the optical trains of the embodiment 300 (presented in Table 3A) and the optical train of the embodiment of the invention 400 (presented in Table 4A) are the same as those discussed in reference to FIGS. 1A, 2A.

In comparison with the design of the illumination relay B of the embodiment 300 of FIG. 3A, and as detailed in Table 4A, the catadioptric illumination relay B-CAT includes one spherical mirror (element 29) and one extra fold planar mirror (element 28). The catadioptric projection lens (A) of either embodiment 300 or 400 also comprises a spherical mirror and a fold mirror, but in addition forms an intermediate image close to the fold mirror (element 14) and a number of aspheric lens elements that, in conjunction with the relay B-CAT, facilitate hyper-NA of 1.35 for the fully-catadioptric embodiment 400 at the immersed in water wafer surface.

Descriptions of aberrations characterizing imaging through the catadioptric lens A of the embodiment 300 of the field framing plane 32 onto the surface of the wafer 1 are presented in FIG. 7A and Table 3B (addressing the ray aberrations, at wavelengths in an approximately 3 pm-wide spectral bandwidth centered at about 193.3 nm, at the plane of the SLM and wavefront aberrations associated with the imaging through the catadioptric lens A of the embodiment 300) and Table 3C (addressing the wavefront aberrations associated with the imaging through the overall optical system of the embodiment 300, between the field framing plane 32 and the surface of the wafer 1). FIG. 7B complements the data of FIG. 7A by providing lots of ray aberrations defined, for the embodiment of FIG. 3A, in the image plane (wafer) within a defined spectral bandwidth around the operating wavelengths. Descriptions of aberrations characterizing imaging through the overall optical system of the embodiment 400 of the invention, between the field framing plane 33 of the embodiment 400 and the surface of the wafer 1 of FIG. 4, are summarized in FIG. 8 and Table 4B (addressing the ray aberrations and wavefront aberrations, respectively). The direct comparison between the data on aberrations for the fully-catadioptric projection lens according to the idea of the invention with those for a conventional lens highlights the advantages of the embodiment of the invention.

As evidenced by the disclosed data, a person of skill in the art will readily appreciate that, for example, the field curvature of the fully-catadioptric design of the invention is substantially reduced compared to that of a conventionally-design system 300. Moreover, the difference between the figures of merits describing the polychromatic aberrations and those describing monochromatic aberrations is substantially smaller for the embodiment 400 of the invention as compared to the embodiment 300. Furthermore, the values of Strehl ratio across the field for the embodiment 400 of the invention are substantially higher than those for the embodiment 300 (see, for example, Strehl ratios respectively characterizing monochromatic rms wavefront aberrations). The embodiment of the invention ensures, in addition to operationally negligible distortion of imaging between the SLM and the wafer, very small residual monochromatic aberrations on the order of about 5 milliwaves rms or less.

It is worth noting that, by structuring the illumination relay of the overall projection system as a catadioptric sub-system, the chromatic aberrations of imaging are substantially reduced in the 50× to 200× dimension reduction system that employs only fused silica refractive optical elements and without the use of complex lenses employing 3 different materials (such as, for example, a classical doublet lens). The reduction of chromatic aberrations results in negligible loss of image contrast when an embodiment of the invention—as compared to a conventionally-designed dioptric-catadioptric projection system—when the system is used with a solid-state laser source the spectral bandwidth of which is on the order of 1 pm FWHM.

Accordingly, embodiments of the present invention provides maskless projection optical systems structured to enable imaging of an object pattern onto a semiconductor wafer with a de-magnification factor of at least 50× and as high as 200×. The projection optics comprises an illumination relay, which projects the UV light of about 193 nm from a field framing plane onto the SLM that reflects the incident light, and a projection lens through which the SLM-reflected UV light is further directed to a semiconductor substrate. The SLM is illuminated by non-telecentric off-axis illumination, and both the illumination relay and the projection lens include a catadioptric optical sub-system to advantageously reduce chromatic aberrations of the system operating in a spectral bandwidth on the order of 1 pm. A fluid is provided between the substrate and the last optical element of the projection lens. The projection optical systems of the invention are configured to enable imaging with an NA of 1.0 or higher.

Example of a Wafer Exposure Apparatus.

An embodiment 900 of the exposure apparatus utilizing an embodiment of the invention is shown in a diagram of FIG. 9, and is equipped with an illumination system 910, a pattern generation device 112, the fully-catadioptric imaging system 902 (such as, for example, an embodiment 200 or 400), a positioning stage device 916, an electronic circuitry governing these and other devices. FIG. 9 illustrates only a schematic of the embodiment, approximately indicating the operable cooperation among the components of the apparatus and not the precise position or orientation of such components, and is not to scale. The exposure apparatus 900 performs an exposure process by projecting an image of a pattern, which is generated by the pattern generation device 112, on a wafer plate (sensitive substrate) W mounted on a stage ST that constitutes a part of the stage device 916, via the catadioptric system of the invention 902, in a scanning fashion that includes synchronization of switching (changing) of a pattern generated by the pattern generation device 912 with movement of the wafer W. The wafer W is scanned in the xy-plane as indicated, with the SLM plane being perpendicular to the plane of the wafer. The exposure apparatus has a degree of freedom to change the angular orientation of the wafer W about the x, y, and z-axes.

The control system includes a data-collection and/or data-processing electronic circuitry (controller) 920 that may be part of a computer processor specifically programmed to govern the operation of the apparatus 900. The control system may be connected to a host device 950 via a communication interface 932.

The illumination system 910 delivers preferably spatially-uniform illumination of a variable molding mask VM, which constitutes a part of the pattern generation device 912, with an illumination (exposure) UV-light IL, and is equipped with: a light source system including at least a UV-light source and a light source control system and an illumination condition-setting mechanism operable to change changing light irradiance distribution at the pupil plane of the illumination optical system; optionally a field stop, a relay lens, and other required zooming, polarizing optical elements as required, among which there may be present an optical integrator (a fly-eye lens), not shown.

The pattern generation device 912 is an electronic mask system that generates a variable pattern to be projected onto the waver W mounted on the stage ST, and is equipped with at least: the variable molding mask VM; a holder 928 that holds the variable molding mask VM; a drive system (controller) 930 that controls operation states of the variable molding mask VM; a tangible, non-transitory and optionally computer-readable memory 933. The mask variable molding mask may generally include a device containing a plurality of micro-reflectors such as, for example, a digital micro-mirror device, known as a DMD, or a 3D MEMS.

The variable molding mask VM is placed above (+Z side) the fully-catadioptric embodiment of the projection system 902, and the illumination light IL is delivered to the system 902 from the illumination system 110 upon reflection from the variable molding mask.

The drive system 930 acquires design data (such as CAD data) of a pattern, required for forming a pattern image on the wafer W, from the host device 950 via the interface 932. The drive system 930 further refers to data (hereinafter, called “signal generation information”) stored in the memory 933, and generates signals to drive the elements/mirrors of the variable molding mask VM based on the design data acquired. The signals to drive each micro mirror are supplied to the driving mechanism of each micro mirror. The drive system 930 can vary patterns to be generated by the variable molding mask VM based on the design data acquired, which may be optionally effectuated synchronously with the movements of the wafer W P mounted on the stage ST.

In addition to the elements of the fully-catadioptric projections system 902 discussed above in reference to the embodiments of FIGS. 2A and 4, an image-forming property compensation device 938 (which drives particular elements inside the fully-catadioptric system 902 in the directions Ax1 AX2 and tilts them according to the provided degrees of angular freedom) may be arranged in operable communication with the system 902. The image-forming property compensation device 938 adjusts image-forming states of the fully catadioptric system 902 of the invention. Alternatively or in addition, wavelength properties of the illumination light IL (such as center of wavelength, spectral bandwidth, and the like) may be controlled to achieve the modification of the image on the wafer W.

The stage device 916 is equipped with: the stage ST that is movable while holding a wafer W (such as a glass substrate, a semiconductor wafer, for example) prepared for exposure; and a stage drive system 940 that controls the operational states (movement and the like) of the stage ST according to commands received from the main controller 920. Positional information (including rotation information) describing the orientation of the stage ST is measured by a positional measurement system (not shown) that may include, for example, a laser interferometer and/or encoder as well as a focus sensor, and is supplied to the main controller 920 which, in turn, drives motors of the stage drive system 940 based on such positional information.

TABLE 1A Description of Optical Train of the Embodiment 100 of FIG. 1A. ELEMENT RADIUS OF CURVATURE APERTURE DIAMETER NUMBER FRONT RACK THICKNESS FRONT PACK GLASS OBJECT INF 3.0000 ‘Water’ 2 INF   −16.2570 CX 13.1558 20.2277 30.2121 ‘SiO2’ 0.2869 3 S(1)   −39.7263 CX 15.3707 46.7684 59.3550 ‘SiO2’ 0.2869 4 S(2)   −60.2724 CX 19.0464 76.1508 82.8331 ‘SiO2’ APERTURE STOP 82.8331 0.2869 5 S(3)   −76.5071 CX 18.2258 90.6356 96.6083 ‘SiO2’ 0.5739 6  359.3759 CX S(4) 23.0773 104.8449 106.5348 ‘SiO2’ 37.1856 7  308.2081 CX  −328.8230 CX 26.5407 102.9433 99.8443 ‘SiO2’ 12.2840 8  89.4404 CX  1362.2325 CC 16.7807 87.4584 83.3926 ‘SiO2’ 8.8213 9 S(5)  −487.6829 CX 7.5000 81.5244 78.3413 ‘SiO2’ 76.8018 10  193.1845 CX   71.5006 CC 5.0000 38.8226 36.4073 ‘SiO2’ 7.6993 11  −39.8835 CC A(1) 5.0000 36.1.057 38.1009 ‘SiO2’ 33.5985 12  382.1002 CX   −77.5554 CX 12.0926 53.9990 55.5152 ‘SiO2’ 1.0000 13 1310.5028 CX A(2) 8.5747 55.3320 55.1363 ‘SiO2’ 50.0953 DECENTER (1) 14 INF −50.2113 C-1 REFL 15 −524.0530 CX A(3) −13.2517 60.2578 61.4956 ‘SiO2’ −206.1572 16  58.8481 CC   115.4857 CX −5.0000 69.6685 75.0749 ‘SiO2’ −1.1717 17 A(4)  −113.4481 CC −5.1548 75.6516 81.7457 ‘SiO2’ −123.3907 18  181.5965 CC 123.2907 185.8623 REFL 19 −113.4481 CC A(5) 5.1648 92.6117 88.5530 ‘SiO2’ 1.1717 20  115.4857 CX   58.8481 CC 5.0000 86.0541 79.2534 ‘SiO2’ 206.1572 21 A(6)  −524.0530 CX 13.2517 93.7414 93.1676 ‘SiO2’ 50.2113 DECENTER( 2) 88.5989 49.9344 22 −128.3482 CC   120.3731 CC 14.6614 68.5771 69.6874 ‘SiO2’ 107.5287 23 A(7)   −86.2586 CX 11.8617 108.0913 112.2249 ‘SiO2’ 502.2967 24 INF −100.0000 216.3994 REFL DECENTER( 3) 25 INF 100.0000 C-2 REFL 26  419.9816 CX  −714.1824 CX 44.9407 282.2641 281.7818 ‘SiO2’ 0.1000 27  216.9230 CX   167.2850 CC 32.4700 261.3636 234.5263 ‘SiO2’ 557.4266 157.5295 0.0000 157.5295 295.3348 28  127.1564 CX −23012.2683 CX 51.4661 112.2159 95.5665 ‘SiO2’ 95.5116 29  −72.8237 CC   84.6697 CC 11.0413 32.0499 30.0404 ‘SiO2’ 27.3428 30  595.1633 CX   −94.4057 CX 76.1582 42.0182 68.5892 ‘SiO2’ 341.1608 31  202.9635 CX  −702.1241 CX 35.0000 136.2980 133.6332 ‘SiO2’ 0.6118 32  99.8742 CX   80.2315 CC 8.0304 125.3481 117.0218 ‘SiO2’ IMAGE DISTANCE = −123.4048 33 IMAGE INF 108.1814 APERTURE DATA DIAMETER DECENTER APERTURE SHAPE X Y X Y ROTATION C-1 RECTANGLE 52.482 20.000 0.000 25.000 0.0 C-2 RECTANGLE 307.113 40 000 0.000 −110.000 0.0 aspheric constants $Z = {\frac{({CURV})Y^{2}}{1 + \left( {1 - {\left( {1 + K} \right)({CURV})^{2}Y^{2}}} \right)^{1/2}} + {(A)Y^{4}} + {(B)Y^{6}} + {(C)Y^{8}} + {(D)Y^{10}} + {(E)Y^{12}} + {(F)Y^{14}} + {(G)Y^{16}} + {(H)Y^{18}} + {(J)Y^{20}}}$ K A B C D ASPHERIC CURV E F G H J A(1)  0.851039E−02 0.00000000 −1.01624E−06  6.08007E−10 −5.62736E−13  1.14084E−15 −2.32923E−18  2.08999E−21  0.00000E+00  0.00000E+00  0.00000E+00 A(2) −0.618726E−02 0.00000000  1.39355E−07  1.13165E−11  7.81414E−16  5.66581E−19  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(3)  0.518760E−02 0.00000000 −8.99477E−08 −2.67713E−12 −8.56400E−16  7.98734E−20  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(4) 0.01015569 0.00000000 −1.65154E−06 −2.76782E-10  1.94297E−13 −5.45936E−17  8.17140E−21 −4.67186E−25  0.00000E+00  0.00000E+00  0.00000E+00 A(5) 0.01015569 0.00000000 −1.65154E−06 −2.76782E−10  1.94297E−13 −5.45936E−17  8.17140E−21 −4.67186E−25  0.00000E+00  0.00000E+00  0.00000E+00 A(6)  0.518760E−02 0.00000000 −8.99477E−08 −2.67713E−12 −8.56400E−16  7.98734E−20  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E−00 A(7) −0.960266E−02 0.00000000  2.22077E−08  1.44665E−12  1.43853E−16  1.09803E−20  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 SPECIAL SURFACES (SPS types) QCN SURFACES x = (Y/NRADIUS)**2 $Z = {\frac{({CURV})Y^{2}}{1 + \left( {1 - {\left( {1 + K} \right)({CURV})^{2}Y^{2}}} \right)^{1/2}} + {x^{2}*\left( {{({QC4}){Q_{0}^{con}(x)}} + {({QC6}){Q_{1}^{con}(x)}} + \ldots + {({QC30}){Q_{13}^{con}(x)}}} \right)}}$ ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(1) −0.393296E−01  0.241104E+02  0.000000E+00  0.102350E+01 −0.110831E+00 −0.153148E−01  0.409086E−02 −0.809714E−03  0.125654E−03 −0.792809E−04  0.106091E−04 −0.131607E−04 −0.914150E−06 −0.301755E−05 −0.558949E−06 −0.106807E−05 −0.437373E−06 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(2) −0.549169E−02  0.410514E+00  0.000000E+00  0.647857E+00 −0.579468E−01 −0.149522E+00 −0.563430E−01 −0.119113E−01 −0.815318E−02 −0.237721E−02 −0.153527E−02 −0.416675E−03 −0.202108E−03 −0.522481E−04 −0.187957E−04 −0.238197E−06  0.192168E−06 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(3) −0.611446E-02  0.480523E+02  0.000000E+00  0.212139E−01 −0.640452E+00  0.290637E+00  0.884384E−01  0.160688E−01 −0.316193E−02 −0.469821E−02 −0.111522E−02  0.393635E−03  0.615198E−03  0.360576E−03  0.142886E−03  0.388167E−04  0.577816E−08 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C5) QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(4) −0.379826E−02  0.559469E+02  0.000000E+00 −0.123020E+01 −0.577347E−01  0.143110E+00  0.581555E−01  0.175100E−01  0.874534E−02  0.409713E−02  0.198654E−02  0.915187E−03  0.409889E−03  0.169900E−03  0.634141E−04  0.198459E−04  0.406977E−05 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(5) −0.546127E−02  0.430941E+02  0.000000E+00 −0.2345 82E+01 −0.409559E−01  0.130732E−02  0.358234E−02  0.144329E−02  0.459955E−03  0.919185E−04 −0.551606E−05 −0.193417E−04 −0.133179E−04 −0.696762E−05 −0.262871E−05 −07092652−06  0.335430E−07 DECENTERING CONSTANTS DECENTER X Y Z ALPHA BETA GAMMA D(1) 0.0000 0.0000 0.0000 45.0000 0.0000 0.0000 (BEND) D 2) 0.0000 0.0000 0.0000 45.0000 0.0000 0.0000 (RETU) D(3) 0.0000 0.0000 0.0000 −45.0000 0.0000 0.0000 (BEND)

TABLE 1B Monochromatic and Polychromatic Wavefront Aberrations and Corresponding Strehl Ratios of the Catadioptric Projection Lens (I, II) of the Embodiment 100 of FIG. 1A. Monochromatic rms wavefront aberrations and Strehl ratio - Wafer to SLM: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.002182 0.0049 0.999 0.000000 0.000635 0.0050 0.999 Y 1.00 0.00 −0.000058 0.000048 X 0.50 0.00 0.000124 0.002561 0.0050 0.999 0.000025 0.000635 0.0051 0.999 Y 1.00 0.00 −0.000165 −0.000033 X 0.70 0.00 −0.000296 −0.003506 0.0027 1.000 0.000003 0.000635 0.0036 1.000 Y 1.00 0.00 0.000282 −0.000003 X 1.00 0.00 0.000065 0.001322 0.0032 1.000 −0.000005 0.000635 0.0032 1.000 Y 1.00 0.00 −0.000044 0.000003 COMPOSITE RMS FOR POSITION 1: 0.00432 Polychromatic rms wavefront aberrations and Strehl ratio - Wafer to SLM: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.011497 0.0206 0.983 0.000000 0.009940 0.0206 0.983 Y 1.00 0.00 −0.000054 0.000053 X 0.50 0.00 0.000121 0.011864 0.0207 0.983 0.000022 0.009940 0.0207 0.983 Y 1.00 0.00 −0.000161 −0.000029 X 0.70 0.00 −0.000300 0.005790 0.0204 0.984 −0.000001 0.009940 0.0205 0.984 Y 1.00 0.00 0.000286 0.000001 X 1.00 0.00 0.000063 0.010627 0.0206 0.983 −0.000007 0.009940 0.0206 0.983 Y 1.00 0.00 −0.000042 0.000005 COMPOSITE RMS FOR POSITION 1: 0.02060 Reduction in Strehl ratio between monochromatic and polychromatic cases represents the contrast loss from chromatic aberrations over the spectral band WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 WTW = 11 29 60 100 69 17 5

TABLE 1C Monochromatic and Polychromatic Wavefront Aberrations and Corresponding Strehl Ratios of the Overall Embodiment 100 of FIG. 1A. Monochromatic rms wavefront aberrations and Strehl ratio - Wafer to field framing plane: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.022771 0.0803 0.775 0.000000 −0.007150 0.1047 0.648 Y 1.00 0.00 0.000621 0.000531 X 0.50 0.00 −0.000104 −0.015071 0.0646 0.848 −0.000101 −0.007150 0.0670 0.838 Y 1.00 0.00 0.000133 0.000155 X 0.70 0.00 0.000071 −0.043989 0.0323 0.960 0.000088 −0.007150 0.0877 0.738 Y 1.00 0.00 −0.000050 0.000044 X 1.00 0.00 0.000823 0.007510 0.0866 0.744 0.000816 −0.007150 0.0923 0.714 Y 1.00 0.00 −0.000533 −0.000579 COMPOSITE RMS FOR POSITION 1: 0.08903 Variation in best individual focus shows the residual field curvature. WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 WTW = 0 0 0 1 0 0 0 Polychromatic rms wavefront aberrations and Strehl ratio - Wafer to field framing plane: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.025445 0.0844 0.755 0.000000 −0.004468 0.1079 0.632 Y 1.00 0.00 0.000606 0.000516 X 0.50 0.00 −0.000096 −0.012416 0.0700 0.824 −0.000094 −0.004468 0.0722 0.814 Y 1.00 0.00 0.000118 0.000140 X 0.70 0.00 0.000081 −0.041317 0.0418 0.933 0.000098 −0.004468 0.0916 0.718 Y 1.00 0.00 −0.000064 0.000030 X 1.00 0.00 0.000833 0.010241 0.0902 0.725 0.000827 −0.004468 0.0958 0.696 Y 1.00 0.00 −0.000544 −0.000590 COMPOSITE RMS FOR POSITION 1: 0.09281 Reduction in Strehl ratio between monochromatic and polychromatic cases represents the contrast loss from chromatic aberrations over the spectral band. Variation in best individual focus shows the residual field curvature. WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 WTW = 11 29 60 100 69 17 5

TABLE 2A Description of Optical Train of the Embodiment 200 of FIG. 2A. ELEMENT RADIUS OF CURVATURE APERTURE DIAMETER NUMBER FRONT BACK THICKNESS FRONT BACK GLASS OBJECT INF 3.0000 ‘Water’ 2 INF  −16.2570 CX 13.1558 20.2277 30.2121 ‘SiO2’ 0.2869 3 S(1)  −39.7263 CX 15.3707 46.7684 59.3550 ‘SiO2’ 0.2869 4 S(2)  −60.2724 CX 19.0464 76.1508 82.8331 ‘SiO2’ APERTURE STOP 82.8331 0.2869 5 S(3)  −76.5071 CX 18.2258 90.6356 96.6083 ‘SiO2’ 0.5739 6  359.3759 CX S(4) 23.0773 104.8449 106.5348 ‘SiO2’ 37.1856 7  308.2081 CX −328.8230 CX 26.5407 102.9433 99.8443 ‘SiO2’ 12.2840 8   89.4404 CX 1362.2325 CC 16.7807 87.4584 83.3926 ‘SiO2’ 8.8213 9 S(5) −487.6829 CX 7.5000 81.5244 78.3413 ‘SiO2’ 76.8018 10  193.1846 CX  71.5006 CC 5.0000 38.8226 36.4073 ‘SiO2’ 7.6993 11  −39.8835 CC A(1) 5.0000 36.1057 38.1009 ‘SiO2’ 33.5985 12  382.1002 CX  −77.5554 CX 12.0926 53.9990 55.5152 ‘SiO2’ 1.0000 13  1310.5028 CX A(2) 8.5747 55.3320 55.1363 ‘SiO2’ 50.0953 DECENTER (1) 14 INF −50.2113 C-1 REFL 15  −524.530 CX A(3) −13.2517 60.2578 61.4956 ‘SiO2’ −206.1572 16   58.8481 CC  115.4857 CX −5.0000 69.6685 75.0749 ‘SiO2’ −1.1717 17 A(4)  −113.4481 CC −5.1648 76.6316 81.7457 ‘SiO2’ −123.3907 18 181.5965 CC 123.3907 185.8623 REFL 19  −113.4481 CC A(5) 5.1648 92.6117 88.5530 ‘SiO2’ 1.1717 20  115.4857 CX  58.8481 CC 5.0000 86.0541 79.2534 ‘SiO2’ 206.1572 21 A(6) −524.0530 CX 13.2517 93.7414 93.1676 ‘SiO2’ 50.2113 DECENTER (2) 88.5989 49.9344 22  −128.3482 CC  120.3731 CC 14.6614 68.5771 69.6874 ‘SiO2’ 107.6287 23 A(7)  −86.2586 CX 11.8617 108.0913 112.2249 ‘SiO2’ 502.2967 24 INF −160.0000 216.3994 REFL DECENTER(3) 25 INF 145.0000 C-2 REFL 26  634.1614 CX −481.4042 CX 60.0000 311.6549 311.6673 ‘SiO2’ 214.8823 27  −253.8821 CC −610.0222 CX 25.0000 225.1467 229.7226 ‘SiO2’ 153.1720 DECENTER( 4) 28 INF −200.0000 C-3 REFL 29 823.1657 CC 353.3051 216.5542 REFL 30  103.1957 CX  77.5662 CC 25.0000 27.3671 31.8654 SiO2’ 145.7979 31 −1301.3477 CC −176.7716 CX 40.0000 115.2141 127.1097 ‘SiO2’ 0.1000 32  226.1976 CX −533.9956 CX 35.0000 131.6026 129.7346 ‘SiO2’ 0.1000 33   96.8063 CX  80.2315 CC 8.0304 122.5221 114.9970 ‘SiO2’ IMAGE DISTANCE = 100.0031 IMAGE INF 108.1987 APERTURE DATA DIAMETER DECENTER APERTURE SHAPE X Y X Y ROTATION C-1 RECTANGLE 52.482 20.000 0.000 25.000 0.0 C-2 RECTANGLE 329.531 50.000 0.000 −120.000 0.0 C-3 RECTANGLE 259.931 50.000 0.000 −813.000 0.0 aspheric constants $Z = {\frac{({CURV})Y^{2}}{1 + \left( {1 - {\left( {1 + K} \right)({CURV})^{2}Y^{2}}} \right)^{1/2}} + {(A)Y^{4}} + {(B)Y^{6}} + {(C)Y^{8}} + {(D)Y^{10}} + {(E)Y^{12}} + {(F)Y^{14}} + {(G)Y^{16}} + {(H)Y^{18}} + {(J)Y^{20}}}$ K A B C D ASPHERIC CURV E F G H J A(1)  0.851039E−02 0.00000000 −1.01624E−06  6.08007E−10 −5.62736E−13  1.14084E−15 −2.32923E−18  2.08999E−21  0.00000E+00  0.00000E+00  0.00000E+00 A(2) −0.618726E−02 0.00000000  1.39355E−07  1.13165E−11  7.81414E−16  5.66581E−19  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(3)  0.518760E−02 0.00000000 −8.99477E−08 −2.67713E−12 −8.56400E−16  7.98734E−20  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(4) 0.01015569 0.00000000 −1.65154E−06 −2.76782E−10  1.94297E−13 −5.45936E−17  8.17140E−21 −4.67186E−25  0.00000E+00  0.00000E+00  0.00000E+00 A(5) 0.01015569 0.00000000 −1.65154E−06 −2.76782E−10  1.94297E−13 −5.45936E−17  8.17140E−21 −4.67186E−25  0.00000E+00  0.00000E+00  0.00000E−00 A(6)  0.518760E−02 0.00000000 −8.994770−08 −2.67713E−12 −8.56400E−36  7.98734E−20  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(7) −0.960266E−02 0.00000000  2.22077E−08  1.44665E−12  1.43851E−16  1.09803E−20  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 SPECIAL SURFACES (SPS types) QCN SURFACES x = (Y/NRADIUS)**2 $Z = {\frac{({CURV})Y^{2}}{1 + \left( {1 - {\left( {1 + K} \right)({CURV})^{2}Y^{2}}} \right)^{1/2}} + {x^{2}*\left( {{({QC4}){Q_{0}^{con}(x)}} + {({QC6}){Q_{1}^{con}(x)}} + \ldots + {({QC30}){Q_{13}^{con}(x)}}} \right)}}$ ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(1) −0.193296E−01  0.241104E+02  0.000000E+00  0.102350E+01 −0.110831E+00 −0.153148E−01  0.409086E−02 −0.809714E−03  0.125654E−03 −0.792809E−04  0.106091E−04 −0.131607E−04 −0.914150E−06 −0.301755E−05 −0.558949E−06 −0.106807E−05 −0.437373E−06 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(2) −0.549169E−02  0.410514E+02  0.000000E+00  0.647857E+00 −0.579468E−01 −0.149522E+00 −0.563430E−01 −0.119113E−01 −0.815318E−02 −0.237721E−02 −0.153527E−02 −0.416675E−03 −0.202108E−03 −0.522481E−04 −0.187957E−04 −0.228197E−06  0.192168E−06 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(3) −0.611446E−02 0.480523E+02 0.000000E+00  0.212139E−01 −0.640452E+00  0.290637E+00 0.884384E−01 0.160688E−01 −0.316193E−02 −0.469821E−02 −0.111522E−02 0.293635E−03 0.615198E−03  0.360576E−03  0.142886E−03  0.388167E−04 0.577816E−05 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(4) −0.379826E−02 0.559469E+02 0.000000E+00 −0.123020E+01 −0.577347E−01 0.142110E+00 0.581555E−01 0.175100E−01  0.874534E−02  0.409713E−02 0.198654E−02 0.91.5187E−03 0.409889E−03  0.1699007−03  0.634341E−04 0.198459E−04 0.406977E−05 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8)  QC14 (C9)  QC16 (C10) QC18 (C11) QC20 (C12) QC22 (C13) QC24 (C14) QC26 (C15) QC28 (C16) QC30 (C17) S(5) −0.546127E−02  0.430941E+02  0.000000E+00 −0.234582E+01 −0.409559E−01  0.130732E−02  0.358234E−02  0.144329E−02  0.459955E−03  0.9191.85E−04 −0.551606E−05 −0.193417E−04 −0.133179E−04 −0.696762E−05 −0.262871E−05 −0.709265E−06  0.335430E−07 DECENTERING CONSTANTS DECENTER X Y Z ALPHA BETA GAMMA D(1) 0.0000 0.0000 0.0000 45.000 0.0000 0.0000 (BEND) D(2) 0.0000 0.0000 0.0000 45.000 0.0000 0.0000 (RETU) D(3) 0.0000 0.0000 0.0000 −45.000 0.0000 0.0000 (BEND) D(4) 0.0000 0.0000 0.0000 −45.000 0.0000 0.0000 (BEND)

TABLE 2B Monochromatic and Polychromatic Wavefront Aberrations and Corresponding Strehl Ratios of the Overall Embodiment 200 of FIG. 2A. Monchromatic rms wavefront aberrations and Strehl ratio - Wafer to field framing plane: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.005621 0.0627 0.856 0.000000 0.000129 0.0639 0.851 Y 1.00 0.00 0.000108 0.000092 X 0.50 0.00 0.000010 −0.006715 0.0254 0.975 0.000012 0.000129 0.0297 0.966 Y 1.00 0.00 0.000071 0.000091 X 0.70 0.00 0.000110 −0.001322 0.0548 0.888 0.000110 0.000129 0.0549 0.888 Y 1.00 0.00 −0.000075 −0.000071 X 1.00 0.00 0.000200 0.002878 0.0510 0.902 0.000199 0.000129 0.0514 0.901 Y 1.00 0.00 −0.000062 −0.000071 COMPOSITE RMS FOR POSITION 1: 0.05156 Variation in best individual focus shows the residual field curvature - much reduced when compared with Dioptric design WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 WTW = 0 0 0 1 0 0 0 Polychromatic rms wavefront aberrations and Strehl ratio - Wafer to field framing plane: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.007964 0.0650 0.846 0.000000 0.002451 0.0662 0.841 Y 1.00 0.00 0.000105 0.000089 X 0.50 0.00 0.000008 −0.004436 0.0317 0.961 0.000010 0.002451 0.0352 0.952 Y 1.00 0.00 0.000068 0.000087 X 0.70 0.00 0.000107 0.000998 0.0584 0.874 0.000108 0.002451 0.0585 0.873 Y 1.00 0.00 −0.000077 −0.000073 X 1.00 0.00 0.000195 0.005229 0.0558 0.884 0.000194 0.002451 0.0562 0.883 Y 1.00 0.00 −0.000063 −0.000072 COMPOSITE RMS FOR POSITION 1: 0.05526 Reduction in Strehl ratio between monochromatic and polychromatic cases represents the contrast loss from chromatic aberrations over the spectral band WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 WTW = 11 29 60 100 69 17 5

TABLE 3A Description of Optical Train of the Embodiment 300 of FIG. 3A. ELEMENT RADIUS OF CURVATURE APERTURE DIAMETER NUMBER FRONT BACK THICKNESS FRONT BACK GLASS OBJECT INF 1.0000 ‘Water’ 2 INF   −8.2303 CX 6.4351 6.5264 1.43201 ‘SiO2’ 0.1435 3 S(1)  −18.8001 CX 6.7222 22.5825 27.5686 ‘SiO2’ 0.1435 4 S(2)  −30.0784 CX 8.5273 35.6362 39.1897 ‘SiO2’ 0.1435 5 S(3)  −38.4857 CX 9.4617 44.1620 46.6075 ‘SiO2’ APERTURE STOP 46.6075 0.2869 6  166.3155 CX S(4) 10.0143 49.0041 49.4058 ‘SiO2’ 23.5239 7  173.2270 CX  −162.8488 CX 7.3700 54.0004 53.9884 ‘SiO2’ 9.4810 8  −154.6474 CC  −86.1299 CX 8.2671 52.1115 52.1002 ‘SiO2’ 0.2096 9 A(1)  −138.6302 CX 3.7500 51.9125 52.2633 ‘SiO2’ 22.8744 10   71.0710 CX  535.1092 CC 6.8489 49.1146 48.1285 ‘SiO2’ 57.9463 11  −54.3888 CC A(2) 29.9969 22.0496 17.8257 ‘SiO2’ 3.7833 12  −53.1248 CC  −32.8926 CX 8.9225 18.0343 19.6876 ‘SiO2’ 11.1925 13  465.4200 CX A(3) 7.3473 19.3068 19.1032 ‘SiO2’ 42.9871 DECENTER (1) 14 INF −43.0547 C-1 REFL 15  −140.8055 CX A(4) −29.9980 26.7472 29.2969 ‘SiO2’ −34.1845 16   59.5352 CC  −59.2154 CC −30.0000 24.5566 26.7873 ‘SiO2’ −13.0243 17 A(5)  −37.3543 CC −2.5824 31.4897 31.9462 ‘SiO2’ −38.4141 18 73.1939 CC 38.4141 56.3111 REFL 19  −37.3543 CC A(6) 2.5824 35.8758 35.8710 ‘SiO2’ 13.0243 20  −59.2154 CC   59.5352 CC 30.0000 31.4408 30.6241 ‘SiO2’ 34.1845 21 A(7)  −140.8055 CX 29.9980 40.2935 38.4955 ‘SiO2’ 43.0547 DECENTER (2) 32.6896 20.0054 22 A(8)   69.7865 CC 16.6301 21.7570 23.4641 ‘SiO2’ 71.5676 23 A(9)  −47.3231 CX 10.8672 45.7252 51.0228 ‘SiO2’ 787.7006 24 INF −50.0000 237.4629 REFL DECENTER ( 3) 25 INF 150.0000 C-2 REFL 26 40540.8039 CX  −491.5484 CX 44.9407 289.1237 292.7506 ‘SiO2’ 0.1000 27  540.7167 CX −3584.5181 CX 35.0000 288.7494 285.5192 ‘SiO2’ 557.4266 30.9950 0.0000 30.9950 448.8330 28  2630.2809 CX  −397.1567 CX 51.4661 192.3463 202.1249 ‘SiO2’ 73.9364 29  168.9589 CX −2918.7765 CX 76.1582 217.9061 200.8210 ‘SiO2’ 7.8995  131.1.316 CX  235.6712 CC 35.0000 166.8410 147.9259 ‘SiO2’ 30 16.5743 31  −652.1637 CC   84.3649 CC 8.0304 147.2153 121.3181 ‘SiO2’ IMAGE DISTANCE = 144.6348 IMAGE INF 118.7353 APERTURE DATA DIAMETER DECENTER APERTURE SHAPE X Y X Y ROTATION C-1 RECTANGLE 19.328 8.000 0.000 9.000 0.0 C-2 RECTANGLE 367.770 50.000 0.000 −170.000 0.0 aspheric constants $Z = {\frac{({CURV})Y^{2}}{1 + \left( {1 - {\left( {1 + K} \right)({CURV})^{2}Y^{2}}} \right)^{1/2}} + {(A)Y^{4}} + {(B)Y^{6}} + {(C)Y^{8}} + {(D)Y^{10}} + {(E)Y^{12}} + {(F)Y^{14}} + {(G)Y^{16}} + {(H)Y^{18}} + {(J)Y^{20}}}$ K A B C D ASPHERIC CURV E F G H J A(1) −0.788036E−02 0.00000000 −1.60680E−06 −5.71603E−30 −7.95423E−13  1.61828E−15 −6.85051E−18  1.52500E−20 −2.15168E−23  1.70021E−26 −5.74938E−30 A(2)  0.03313618 0.00000000 −1.12080E−05  3.59225E−08 −8.31387E−11 −8.58999E−13  3.01032E−15  6.97263E−18  0.00000E+00  0.00000E+00  0.00000E+00 A(3) −0.01807134 0.00000000  2.44282E−07 −5.88773E−09  1.90874E−11  5.73753E−15  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(4)  0.01839303 0.00000000 −2.40018E−06  1.13544E−09 −1.07358E−12  6.87182E−16  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(5)  0.206863E−02 0.00000000 −1.78913E−05  1.98684E−09  2.29867E−11 −5.17522E−14  5.67365E−17 −2.60781E−20  0.00000E+00  0.00000E+00  0.00000E+00 A(6)  0.206863E−02 0.00000000 −1.78913E−05  1.98684E−09  2.29867E−11 −5.17522E−14  5.67365E−17 −2.60781E−20  0.00000E+00  0.00000E+00  0.00000E+00 A(7)  0.03839301 0 .00000000 −2.40018E−06  1.33544E−09 −1.07358E−12  6.87182E−16  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(8) −0.02941486 0.00000000 −9.82126E−07 −6.38630E−09  2.82716E−11 −1.59921E−13  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(9) −0.02047184 0.00000000  7.86549E−08  1.18534E−10 −1.77852E−13  1.38406E−16  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 SPECIAL SURFACES (SPS types) QCN SURFACES x = (Y/NRADIUS)**2 $Z = {\frac{({CURV})Y^{2}}{1 + \left( {1 - {\left( {1 + K} \right)({CURV})^{2}Y^{2}}} \right)^{1/2}} + {x^{2}*\left( {{({QC4}){Q_{0}^{con}(x)}} + {({QC6}){Q_{1}^{con}(x)}} + \ldots + {({QC30}){Q_{13}^{con}(x)}}} \right)}}$ ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8) QC14 (C9) QC16 (C10) QC18 (C11) QC20 (C12) S(1) −0.375089E−01  0.117087E+02  0.000000E+00  0.781699E+00 −0.111327E+00 −0.752173E−02  0.189059E−02 −0.165226E−02  0.132330E−03 −0.400665E−04 −0.154608E−04  0.381404E−05 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8) QC14 (C9) QC16 (C10) QC18 (C11) QC20 (C12) S(2) −0.108880E−01  0.189520E+02  0.000000E+00  0.179588E+00 −0.243968E+00  0.129881E+00 −0.269953E−01  0.723456E−02 −0.134297E−02  0.138474E−03 −0.167556E−03  0.920416E−05 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8) QC14 (C9) QC16 (C10) QC18 (C11) QC20 (C12) S(3) −0.323451E−01  0.220374E+02  0.000000E+00  0.673702E+00  0.232005E+00 −0.718514E−01  0.108260E−01 −0.224315E−03 −0.855525E−03  0.320809E−04  0.801810E−04 −0.195269E−04 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8) QC14 (C9) QC16 (C10) QC18 (C11) QC20 (C12) S(4) −0.810124E−02  0.230971E+02  0.000000E+00  0.101446E+01  0.356972E−01 −0.207860E−02  0.217109E−02  0.423426E−03  0.307139E−04 −0.463203E−05  0.168129E−05 −0.616318E−06 DECENTERING CONSTANTS DECENT X Y Z ALPHA BETA GAMMA D(1) 0.0000 0.0000 0.0000 45.0000 0.0000 0.0000 (BEND) D(2) 0.0000 0.0000 0.0000 45.0000 0.0000 0.0000 (RETU) D(3) 0.0000 0.0000 0.0000 −45.0000 0.0000 0.0000 (BEND)

TABLE 3B Monochromatic and Polychromatic Wavefront Aberrations and Corresponding Strehl Ratios of the Catadioptric Projection Lens (I, II) of the Embodiment 300 of FIG. 3A. Monochromatic rms wavefront aberrations and Strehl ratio - Wafer to SLM: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.039535 0.0022 1.000 0.000000 0.002739 0.0026 1.000 Y 1.00 0.00 −0.003775 0.000046 X 0.50 0.00 −0.000803 −0.021277 0.0008 1.000 −0.000004 0.002739 0.0011 1.000 Y 1.00 0.00 0.002507 0.000013 X 0.70 0.00 −0.001107 −0.021449 0.0017 1.000 0.000018 0.002739 0.0019 1.000 Y 1.00 0.00 0.002472 −0.000040 X 1.00 0.00 0.000754 0.014220 0.0011 1.000 −0.000008 0.002739 0.0011 1.000 Y 1.00 0.00 −0.001178 0.000014 COMPOSITE RMS FOR POSITION 1: 0.00178 WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 nm WTW = 0 0 0 1 0 0 0 Polychromatic rms wavefront aberrations and Strehl ratio- Wafer to SLM: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM) (WAVES) STREHL X 0.00 0.00 0.000000 0.171069 0.0173 0.988 0.000000 0.133909 0.0173 0.988 Y 1.00 0.00 −0.003792 0.000067 X 0.50 0.00 −0.000805 0.110031 0.0172 0.988 −0.000011 0.133909 0.0172 0.988 Y 1.00 0.00 0.002513 0.000034 X 0.70 0.00 −0.001119 0.109673 0.0172 0.988 0.000009 0.133909 0.0172 0.988 Y 1.00 0.00 0.002497 −0.000020 X 1.00 0.00 0.000711 0.144938 0.0172 0.988 −0.000021 0.133909 0.0172 0.988 Y 1.00 0.00 −0.001111 0.000034 COMPOSITE RMS FOR POSITION 1: 0.01723 Reduction in Strehl ratio between monochromatic and polychromatic cases represents the contrast loss from chromatic aberrations over the spectral band WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 WTW = 11 29 60 100 69 17 5

TABLE 3C Monochromatic and Polychromatic Wavefront Aberrations and Corresponding Strehl Ratios of the Overall Embodiment 300 of FIG. 3A. Monochromatic rms wavefront aberrations and Strehl ratio - Wafer to field framing plane: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.041154 0.0228 0.980 0.000000 −0.002362 0.0236 0.978 Y 1.00 0.00 0.000279 0.000268 X 0.50 0.00 −0.000064 0.017039 0.0056 0.999 −0.000064 −0.002362 0.0062 0.998 Y 1.00 0.00 0.000207 0.000209 X 0.70 0.00 −0.000053 0.009362 0.0112 0.995 −0.000054 −0.002362 0.0113 0.995 Y 1.00 0.00 0.000121 0.000124 X 1.00 0.00 0.000235 −0.083257 0.0165 0.989 0.000230 −0.002362 0.0197 0.985 Y 1.00 0.00 −0.000371 −0.000364 COMPOSITE RMS FOR POSITION 1: 0.01670 Variation in best individual focus shows the residual field curvature WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 WTW = 0 0 0 1 0 0 0 Polychromatic rms wavefront aberrations and Strehl ratio - Wafer to field framing plane: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.075248 0.0289 0.967 0.000000 0.032115 0.0295 0.966 Y 1.00 0.00 0.000307 0.000296 X 0.50 0.00 −0.000073 0.051169 0.0186 0.986 −0.000074 0.032115 0.0188 0.986 Y 1.00 0.00 0.000236 0.000238 X 0.70 0.00 −0.000067 0.043788 0.0212 0.982 −0.000068 0.032115 0.0212 0.982 Y 1.00 0.00 0.000151 0.000154 X 1.00 0.00 0.000213 −0.047939 0.0248 0.976 0.000208 0.032115 0.0270 0.972 Y 1.00 0.00 −0.000337 −0.000330 COMPOSITE RMS FOR POSITION 1: 0.02453 Variation in best individual focus shows the residual field curvature Reduction in Strehl ratio between monochromatic and polychromatic cases represents the contrast loss from chromatic aberrations over the spectral band WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 WTW = 11 29 60 100 69 17 5

TABLE 4A Description of Optical Train of the Embodiment 400 of FIG. 4. ELEMENT RADIUS OF CURVATURE APERTURE DIAMETER NUMBER FRONT BACK THICKNESS FRONT BACK GLASS OBJECT INF 1.0000 ‘Water’ 2 INF  −8.2303 CX 6.4351 6.5264 14.3201 ‘SiO2’ 0.1435 3 S(1)  −18.8001 CX 6.7222 22.5825 27.5686 ‘SiO2’ 0.1435 4 S(2)  −30.0784 CX 8.5273 35.6362 39.1897 ‘SiO2’ 0.1435 5 S(3)  −38.4857 CX 9.4617 44.1620 46.6075 ‘SiO2’ APERTURE STOP 46.6075 0.2869 6  166.3155 CX S(4) 10.0143 49.0041 49.4058 ‘SiO2’ 23.5239 7  173.2270 CX −162.8488 CX 7.3700 54.0004 53.9884 ‘SiO2’ 9.4810 8 −154.6474 CC  −86.1299 CX 8.2671 52.1115 52.1002 ‘SiO2’ 0.2096 9 A(1)  −138.6302 CX 3.7500 51.9125 52.2633 ‘SiO2’ 22.8744 10  71.0710 CX  535.1092 CC 6.8489 49.1146 48.1285 ‘SiO2’ 57.9463 11  −54.3888 CC A(2) 29.9969 22.0496 17.8257 ‘SiO2’ 3.7833 12  −53.1248 CC  −32.8926 CX 8.9225 18.0343 19.6876 ‘SiO2’ 11.1925 13  465.4200 CX A(3) 7.3473 19.3068 19.1032 ‘SiO2’ 42.9871 DECENTER (1) 14 INF −43.0547 C-1 REFL 15  −140.8055 CX A(4) −29.9980 26.7472 29.2969 ‘SiO2’ −34.1845 16  59.5352 CC  −59.2154 CC −30.0000 24.5566 26.7873 ‘SiO2’ −13.0243 17 A(5)  −37.3543 CC −2.5824 31.4897 31.9462 ‘SiO2’ −38.4141 18 73.1939 CC 38.4141 56.3111 REFL 19  −37.3543 CC A(6) 2.5824 35.8758 35.8710 ‘SiO2’ 13.0243 20  −59.2154 CC  59.5352 CC 30.0000 31.4408 30.6241 ‘SiO2’ 34.1845 21 A(7) −140.8055 CX 29.9980 40.2935 38.4955 ‘SiO2’ 43.0547 DECENTER( 2) 32.6896 20.0054 22 A(8)  69.7865 CC 16.6301 21.7570 23.4641 ‘SiO2’ 71.5676 23 A(9)  −47.3231 CX 10.8672 45.7252 51.0228 ‘SiO2’ 787.7006 24 INF −50.0000 237.4629 REFL DECENTER (3) 25 INF 150.0000 C-2 REFL 26 1020.7892 CX −440.5935 CX 44.9407 291.7619 292.3223 ‘SiO2’ 86.9784 27 −282.8413 CC −409.0313 CX 35.0000 267.7683 276.3214 ‘SiO2’ 457.4266 DECENTER (4) 28 INF −100.0000 C-3 REFL 29 754.6155 CC 361.7155 218.6596 REFL 30 −813.6819 CC  98.9319 CC 19.7149 39.3317 49.4552 ‘SiO2’ 3.9591 31 −981.5537 CC  −89.9106 CX 20.0000 50.0401 60.6842 ‘SiO2’ 79.9587 32 −793.5946 CC −101.2088 CX 23.0169 119.0006 121.4729 ‘SiO2’ IMAGE DISTANCE = 100.0000 IMAGE INF 118.6588 APERTURE DATA DIAMETER DECENTER APERTURE SHAPE X Y X Y ROTATION C-1 RECTANGLE 19.328 8.000 0.000 9.000 0.0 C-2 RECTANGLE 367.770 40.000 0.000 −160.000 0.0 C-3 RECTANGLE 312.758 60.000 0.000 −140.000 0.0 aspheric constants $Z = {\frac{({CURV})Y^{2}}{1 + \left( {1 - {\left( {1 + K} \right)({CURV})^{2}Y^{2}}} \right)^{1/2}} + {(A)Y^{4}} + {(B)Y^{6}} + {(C)Y^{8}} + {(D)Y^{10}} + {(E)Y^{12}} + {(F)Y^{14}} + {(G)Y^{16}} + {(H)Y^{18}} + {(J)Y^{20}}}$ K A E C D ASPHERIC CURV E F G H J A(1) −0.788036E−02 0.00000000 −1.60680E−06 −5.71603E−10 −7.95421E−13  1.61828E−15 −6.85053E−18  1.52500E−20 −2.15168E−23  1.70023E-26 −5.74938E−30 A(2)  0.0331618 0.00000000 −1.12080E−05  3.59225E−08 −8.31387E−11 −8.58999E−13  3.01032E−15  6.97263E−18  0.00000E+00  0.00000E+00  0.00000E+00 A(3) −0.01807134 0.00000000  2.44282E−07 −5.88773E−09  1.90874E−11  5.73753E−15  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(4)  0.01839301 0.00000000 −2.40018E−06  1.13544E−09 −1.07358E−12  6.87182E−16  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(5)  0.206863E−02 0.00000000 −1.78913E−05  1.98684E−09  2.29867E−11 −5.17522E−14  5.67365E−17 −2.60781E−20  0.00000E+00  0.00000E+00  0.00000E+00 A(6)  0.206863E−02 0.00000000 −1.78913E−05  1.98684E−09  2.29867E−11 −5.17522E−14  5.67365E−17 −2.60781E−20  0.00000E+00  0.00000E+00  0.00000E+00 A(7)  0.01839301 0.00000000 −2.40018E−06  1.13544E−09 −1.07358E−12  6.87182E−16  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(8) −0.02941486 0.00000000 −9.82126E−07 −6.38630E−09  2.82716E−11 −1.59923E−13  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 A(9) −0.02047184 0.00000000  7.86549E−08  1.18534E−10 −1.77852E−13  1.38406E−16  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00 SPECIAL SURFACES (SPS types) QCN SURFACES x - (Y/NRADIUS)**2 $Z = {\frac{({CURV})Y^{2}}{1 + \left( {1 - {\left( {1 + K} \right)({CURV})^{2}Y^{2}}} \right)^{1/2}} + {x^{2}*\left( {{({QC4}){Q_{0}^{con}(x)}} + {({QC6}){Q_{1}^{con}(x)}} + \ldots + {({QC30}){Q_{13}^{con}(x)}}} \right)}}$ ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8) QC14 (C9) QC16 (C10) QC18 (C11) QC20 (C12) S(1) −0.375089E−01  0.117087E+02  0.000000E+00  0.781699E+00 −0.111327E+00 −0.752173E−02  0.189059E−02 −0.165226E−02  0.132330E−03 −0.400665E−04 −0.154608E−04  0.381404E−05 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8) QC14 (C9) QC16 (C10) QC18 (C11) QC20 (C12) S(2) −0.108880E−01  0.189520E+02  0.000000E+00  0.179588E+00 −0.243968E+00  0.129881E+00 −0.269953E−01  0.723456E−02 −0.134297E−02  0.138474E−03 −0.167556E−03  0.920416E-05 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8) QC14 (C9) QC16 (C10) QC18 (C11) QC20 (C12) S(3) −0.123451E−01  0.220374E+02  0.000000E+00  0.673702E+00  0.232005E+00 −0.718514E−01  0.108260E−01 −0.224315E−03 −0.855525E−03  0.320809E−04  0.801810E−04 −0.195269E−04 ASPHERIC CURV NRADIUS (C2) K (C1) QC4 (C4)  QC6 (C5)  QC8 (C6)  QC10 (C7)  QC12 (C8) QC14 (C9) QC16 (C10) QC18 (C11) QC20 (C12) S(4) −0.810124E−02  0.230971E+02  0.000000E+00  0.101446E+01  0.356972E−01 −0.207860E−02  0.217109E−02  0.423426E−03  0.307139E−04 −0.463203E−05  0.1681E9E−05 −0.616318E−06 DECENTERING CONSTANTS DECENTER X Y Z ALPHA BETA GAMMA D(1) 0.0000 0.0000 0.0000 45.0000 0.0000 0.0000 (BEND) D(2) 0.0000 0.0000 0.0000 45.0000 0.0000 0.0000 (RETU) D(3) 0.0000 0.0000 0.0000 −45.0000 0.0000 0.0000 (BEND) D(4) 0.0000 0.0000 0.0000 −45.0000 0.0000 0.0000 (BEND)

TABLE 4B Monochromatic and Polychromatic Wavefront Aberrations and Corresponding Strehl Ratios of the Overall Embodiment 400 of FIG. 4. Monochromatic rms wavefront aberrations and Strehl ratio - Wafer to field framing plane: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.007905 0.0078 0.998 0.000000 −0.002581 0.0079 0.998 Y 1.00 0.00 −0.000181 −0.000182 X 0.50 0.00 0.000030 −0.006455 0.0033 1.000 0.000030 −0.002581 0.0033 1.000 Y 1.00 0.00 −0.000074 −0.000074 X 0.70 0.00 −0.000008 −0.002172 0.0061 0.999 −0.000008 −0.002581 0.0061 0.999 Y 1.00 0.00 0.000032 0.000032 X 1.00 0.00 −0.000080 −0.009028 0.0040 0.999 −0.000080 −0.002581 0.0041 0.999 Y 1.00 0.00 0.000132 0.000133 COMPOSITE RMS FOR POSITION 1: 0.00565 Variation in best individual focus shows the residual field curvature - much reduced when compared with Dioptric design WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 nm WTW = 0 0 0 1 0 0 0 Polychromatic rms wavefront aberrations and Strehl ratio - Wafer to field framing plane: BEST INDIVIDUAL FOCUS BEST COMPOSITE FOCUS SHIFT FOCUS RMS SHIFT FOCUS RMS FIELD FRACT DEG (MM.) (MM.) (WAVES) STREHL (MM.) (MM.) (WAVES) STREHL X 0.00 0.00 0.000000 0.041360 0.0188 0.986 0.000000 0.030520 0.0189 0.986 Y 1.00 0.00 −0.000182 −0.000182 X 0.50 0.00 0.000030 0.026927 0.0175 0.988 0.000030 0.030520 0.0175 0.988 Y 1.00 0.00 −0.000074 −0.000074 X 0.70 0.00 −0.000008 0.030934 0.0181 0.987 −0.000008 0.030520 0.0181 0.987 Y 1.00 0.00 0.000032 0.000032 X 1.00 0.00 −0.000081 0.023475 0.0175 0.988 −0.000081 0.030520 0.0175 0.988 Y 1.00 0.00 0.000134 0.000134 COMPOSITE RMS FOR POSITION 1: 0.01801 Reduction in Strehl ratio between monochromatic and polychromatic cases represents the contrast loss from chromatic aberrations over the spectral band WL = 193.3074 193.3069 193.3065 193.306 193.3057 193.3055 193.3046 nm WTW = 11 29 60 100 69 17 5

In one specific implementation of the projection optical system of the invention, the catadioptric projection lens is made to include first and second portions (such as, for example, portions I and II of the embodiment 200) such that the second portion is structured as a catadioptric optical system forming, in light received from the catadioptric illumination relay lens, an intermediate optical image at a location between elements of the second portion. In such specific implementation, the first portion of the catadioptric projection lens is structured as a dioptric optical unit disposed to transfer light from the location of the intermediate image to an image plane of the projection optical system to form of the intermediate optical image at the image plan. Such specific catadioptric projection lens is configured to satisfy a condition of

$\begin{matrix} {{A < \frac{\beta_{I}}{\beta_{T}} < B},} & (1) \end{matrix}$

where β_(I) denotes a magnification of the first portion of the catadioptric projection lens, β_(T) denotes a magnification of the whole catadioptric projection lens, A=4, B=30. As would be appreciated by a person of skill in the art, this implementation possesses an unexpected operational advantage over a catadioptric projection lens of a related art in that it avoids a situation of

${\frac{\beta_{I}}{\beta_{T}} > 30},$ when the required value of the NA of the second portion is too large for practical purposes such that correction of aberrations of the catadioptric projection lens becomes prohibitively expensive. At the same time, by keeping the ratio of

$\frac{\beta_{I}}{\beta_{T}}$ above 4, the magnification value of the first portion is keep from becoming so impractically large as to make it cost prohibitive to correct aberrations of the projection optical system. It may be preferred to set A=5 and B=25 for high optical performance of the projection optical system; and even more preferred to set B=21.

In another related specific implementation of the projection optical system of the invention, the catadioptric projection lens is structured to include first and second portions as discussed above and to satisfy a condition of

$\begin{matrix} {{C < \frac{\beta_{II}}{\beta_{T}} < D},} & (2) \end{matrix}$

where β_(I) denotes a magnification of the first portion of the catadioptric projection lens and C=6 and D=20. As would be appreciated by a person of skill in the art, this implementation possesses an unexpected operational advantage over a catadioptric projection lens of a related art in that it avoids a situation when the total length of the second portion is prohibitively large from the operational standpoint and when the magnification of the first portion is too high. (Such impractical situation corresponds to D>20 and is accompanied by aberrations of the projection optical system that are too high to correct at operationally reasonable cost.) At the same time, this specific implementation is operationally advantageous over the similar system characterized by

$C < \frac{\beta_{II}}{\beta_{T}}$ where C<6, for which the value of NA of the second portion is so high that the resulting aberrations are impractical to correct. For high optical performance of the projection optical system of the invention, it may be preferred to set C=5; to improve the operational characteristics even further, the lower limit of condition (2) may be set to 7.7. yet in a more preferred embodiment, the upper limit D may be set to 14.

In yet another related specific implementation of the projection optical system of the invention, the catadioptric projection lens is structured to include a first and second portions as discussed above and to satisfy a condition of |β_(II)|<|β_(I)|,  (3)

to ensure high optical performance in conjunction with the digital scanner as disclosed above.

The following Table 5 illustrates non-limiting examples pertaining to configurations of the catadioptric projection lens of the projection optical system of the invention:

TABLE 5 Condition Example A Example B Example C Example D |β_(I)| 0.1 0.1 0.1 0.1 |β_(II)| 0.2 0.2 0.05 0.05 |β_(T)| 0.02 0.02 0.005 0.005 |β_(I)|/|β_(T)| 5 5 20 20 |β_(II)|/β_(T)| 10 10 10 10

An example of forming an optical image with an embodiment of the projection optical system according to the invention is schematically illustrated by a flow-chart 1000 in FIG. 10. At step 1010, radiation that has been transmitted through a catadioptric illumination relay system structured according to an embodiment of the invention as discussed above is received with an SLM. At step 1020, radiation received by the SLM through a catadioptric projection lens of the embodiment is reflected by the SLM to form an image such that chromatic errors induced in the image are at least partially reduced. As a result of such reflection, an intermediate image of an object irradiated with the radiation can be formed within the catadioptric projection lens (for example, between the elements of such lens). The intermediate image is further re-imaged, at step 1030, through the catadioptric projection lens and fluid or liquid to form as image of the object at the image plane. Optionally, at step 1040, a beam defined by the radiation received at the SLM, is digitally scanned (for example, with a digital scanner system used in conjunction with the embodiment). The radiation at hand may have a bandwidth on the order of 1 picometer, in one implementation from about half a picometer to several picometers (for example, 5 picometers).

It is notable, that a second portion of a catadioptric projection lens of an embodiments of the invention includes the combination of the two negative lenses 16, 17 (see, for example, the portion labeled II in the embodiment of FIG. 2A or that of FIG. 4, the projection lens of which is structured in a similar fashion) and, for that reason, is configured differently from similar portion that related art has been utilizing to date. In particular, catadioptric projection lenses of the projection systems of the related art include only one, single lens in place of the combination of lenses 16, 17 used herein. Such single lens is known to some as a Schupmann lens, which conventionally, is a single negative-power meniscus lens element placed close to a concave mirror of the projection lens. According to the idea of the present invention, two such lens elements are used instead, which provides the proposed designed with more degrees of freedom for correction of aberrations, in particular spherical aberration and coma. (For proper comparison of the operation of the embodiments of FIGS. 2A, 2B and 4 with projection systems of FIGS. 1A-1C and 3A-3C that are structured conventionally, the combination of two negative-power meniscus elements in used in each of the corresponding catadioptric projection lens. See also data in the Tables.)

The embodiments discussed above may be employed with an exposure apparatus that is disclosed, for example, in U.S. Pat. No. 8,089,616, and U.S. Patent Application Publications Nos. 2013/0278912, 2013/0314683, 2013/0222781, and 2014/0320835. The disclosure of each of these patent documents is incorporated by reference herein. The discussed embodiments may be also utilized in a polarization illuminating optical system that is disclosed in, for example, U.S. Patent Application Publications Nos. 2013/0146676, 2014/0211174, and 2014/0233008. The disclosure of each of these patent documents is also incorporated by reference herein.

It is appreciated that either of the illumination optical system, or the projection optical system of the embodiments discussed above, and the exposure apparatus is produced by assembling various subsystems including the constituent elements and units recited in the appended claims so that the predetermined mechanical accuracy, the accuracy of electrical and optical performance of the resulting assembly are maintained. In order to ensure such accurate operational performance, various operational adjustments may be carried out before and/or after the assembly has been completed, including adjustments for achieving the required optical accuracy for various optical elements and systems, adjustments for achieving the required mechanical accuracy for various mechanical systems, and adjustments for achieving the required electrical accuracy for various electrical systems. The steps of assembling various subsystems into the exposure apparatus include, for example, establishing mechanical connections among the components, establishing wiring connections among the electric circuits, and establishing piping connections effectuating air pressure circuits among the various subsystems. The assembling process of the individual subsystems is performed before the assembly of various subsystems into the overall exposure apparatus. When the assembly of the exposure apparatus is completed, the overall adjustment procedure is effectuated to secure the accurate operational performance of the entire exposure apparatus. It is also appropriate for the exposure apparatus to be produced in a clean room in which, for example, the temperature and the purity of environment are managed.

Embodiments of the present invention are not limited for use with an exposure apparatus configured to produce a semiconductor device, but are also widely applicable, for example, to an exposure apparatus configured to produce a liquid crystal display device formed on a rectangular glass plate, or a display apparatus such as the plasma display, as well as an exposure apparatus configured to produce an the image-pickup device (for example, a CCD), a micromachine, a thin-film magnetic head, and a DNA chip. Embodiments of the present invention can also be employed at the exposure step to be used when the mask (such as a photomask and/or a reticle) formed with the mask-pattern is produced photolithographically.

In the embodiments described above, a used light source may be configured, in a specific case, to emit UV light at a wavelength of 193 nm and a spectral bandwidth on the order of 0.1 pm (measured as full-width-half-maximum, or FWHM, value). Generally, however, another appropriate laser light source may be employed, including, for example, an ArF excimer laser source for supplying the laser beam at 193 nm, an KrF excimer laser light for supplying the laser beam at 248 nm, an F₂ laser light source for supplying the laser beam at 157 nm, the pulsed laser light source such as the Ar₂ laser (with output wavelength of 126 nm), a Kr₂ laser (with output wavelength of 146 nm), the g-ray source (wavelength of 436 nm), an YAG laser cooperated with a light-harmonic generator, and an ultra-high pressure mercury lamp configured to generate at 365 nm. As disclosed in the U.S. Pat. No. 7,023,610, it is also appropriate to use a harmonic wave as the vacuum ultraviolet light (such harmonic wave being obtained by i) amplifying a single wavelength laser beam in the infrared or visible spectral region produced by a fiber laser or a DFB semiconductor laser with, for example, a fiber amplifier doped with erbium and/or ytterbium and ii) performing the wavelength conversion into the ultraviolet spectral region by using principles of non-linear optics, for example utilizing a nonlinear optical crystal. The disclosure of U.S. Pat. No. 7,023,610 is incorporated by reference herein.

References made throughout this specification to “one embodiment,” “an embodiment,” “a related embodiment,” or similar language mean that a particular feature, structure, or characteristic described in connection with the referred to “embodiment” is included in at least one embodiment of the present invention. Thus, appearances of these phrases and terms may, but do not necessarily, refer to the same implementation. It is to be understood that no portion of disclosure, taken on its own and in possible connection with a figure, is intended to provide a complete description of all features of the invention.

It is also to be understood that no single drawing is intended to support a complete description of all features of the invention. In other words, a given drawing is generally descriptive of only some, and generally not all, features of the invention. A given drawing and an associated portion of the disclosure containing a description referencing such drawing do not, generally, contain all elements of a particular view or all features that can be presented is this view, for purposes of simplifying the given drawing and discussion, and to direct the discussion to particular elements that are featured in this drawing. A skilled artisan will recognize that the invention may possibly be practiced without one or more of the specific features, elements, components, structures, details, or characteristics, or with the use of other methods, components, materials, and so forth. Therefore, although a particular detail of an embodiment of the invention may not be necessarily shown in each and every drawing describing such embodiment, the presence of this detail in the drawing may be implied unless the context of the description requires otherwise. In other instances, well known structures, details, materials, or operations may be not shown in a given drawing or described in detail to avoid obscuring aspects of an embodiment of the invention that are being discussed.

The invention as recited in claims appended to this disclosure is intended to be assessed in light of the disclosure as a whole, including features disclosed in prior art to which reference is made.

While the description of the invention is presented through the above examples of embodiments, those of ordinary skill in the art understand that modifications to, and variations of, the illustrated embodiments may be made without departing from the inventive concepts disclosed herein. The invention should not be viewed as being limited to the disclosed examples. 

What is claimed is:
 1. A projection optical system configured to form an image on an image plane, comprising: a first optical system having a concave mirror, said first optical system configured to form an intermediate optical image; a second optical system configured as a dioptric optical system disposed to form an image of the intermediate image on the image plane; said first and second optical systems aggregately configured to satisfy a condition of ${4 < \frac{\beta_{I}}{\beta_{T}} < 30},$  wherein β_(I) denotes a magnification of the second optical system and β_(T) denotes a magnification of the projection optical system.
 2. A projection optical system according to claim 1, further comprising a catadioptric illumination relay lens and a spatial light modulator (SLM) positioned to receive light from the catadioptric illumination relay lens and reflect said light towards the first and second optical systems.
 3. A projection optical system according to claim 1, wherein said projection optical system is configured to satisfy a condition of ${6 < \frac{\beta_{II}}{\beta_{T}} < 20},$  wherein β_(II) denotes a magnification of the first optical system.
 4. A projection optical system according to claim 1, wherein said projection optical system is configured to satisfy a condition of |β_(II)|<|β_(I)|, wherein β_(II) denotes a magnification of the first optical system.
 5. A projection optical system according to claim 1, wherein said first optical system is configured such that said light directed through the projection optical system towards the image plane passes through a first group of lenses including a first negative lens, then through a second group of lenses, and then is reflected with a concave mirror to form a reflected beam transmitted through the second group of lenses.
 6. A projection optical system according to claim 5, wherein the second group of lenses includes second and third negative lenses immediately adjacent to one another, a concave surface of the second negative lens facing away from the concave mirror, a concave surface of the third negative lens facing the concave mirror.
 7. A projection optical system according to claim 6, wherein the second group of lenses further comprises a positive lens between the first group of lenses and the third negative lens.
 8. A projection optical system according to claim 1, wherein the second optical system comprises at least two positive lenses disposed immediately adjacent to one another such as to receive light directly from the intermediate image.
 9. A projection optical system according to claim 8, wherein the second optical system further comprises at least two negative lenses disposed immediately adjacent to one another between said at least two positive lenses and the image plane.
 10. A projection optical system according to claim 9, wherein the second optical system further comprises a light-condensing lens unit between the at least two negative lenses and the image plane.
 11. A projection optical system according to claim 10, wherein every lens of the light-condensing lens-unit is a positive lens.
 12. A projection optical system according to claim 1, characterized, in operation with light having a central wavelength of about 193.3 nm and a spectral bandwidth of about 1 picometer, a first Strehl ratio at the central wavelength and a second Strehl ratio across the spectral bandwidth, both the first and second Strehl ratios exceeding 0.95.
 13. A projection optical system according to claim 1, configured to form the image with a reduction ratio of at least
 50. 14. An exposure apparatus configured to expose a substrate to light delivered thereto through liquid from an object, said exposure apparatus comprising: a stage configured to support a substrate defining an image plane; and a projection optical system comprising: a first optical system having a concave mirror, said first optical system configured to form an intermediate optical image; a second optical system configured as a dioptric optical system disposed to form an image of the intermediate image on the image plane; said first and second optical systems aggregately configured to satisfy a condition of ${4 < \frac{\beta_{I}}{\beta_{T}} < 30},$  wherein β_(I) denotes a magnification of the second optical system and β_(T) denotes a magnification of the projection optical system; wherein said exposure apparatus is configured to form said image of the intermediate image on the substrate with light transmitted from an object through the projection optical system and liquid between the projection optical system and the substrate.
 15. An exposure apparatus according to claim 14, further comprising an illumination relay lens disposed to illuminate the object with the light passing therethrough.
 16. An exposure apparatus according to claim 15, wherein said illumination relay lens includes a catadioptric illumination relay lens.
 17. A method for manufacturing a device, the method comprising: exposing a substrate with light delivered thereto from an object through liquid with the use of the projection optical system that comprises a first optical system having a concave mirror, said first optical system configured to form an intermediate optical image; a second optical system configured as a dioptric optical system disposed to form an image of the intermediate image on the image plane; wherein said first and second optical systems are aggregately configured to satisfy a condition of ${4 < \frac{\beta_{I}}{\beta_{T}} < 30},$  wherein β_(I) denotes a magnification of the second optical system and β_(T) denotes a magnification of the projection optical system; and developing said substrate after said exposing.
 18. A projection optical system configured to form an image on an image plane, the projection optical system comprising: a first optical system including a concave mirror positioned to form an intermediate optical image; a second optical system configured as a dioptric optical system and disposed to form an image of the intermediate image on the image plane; said first and second optical systems aggregately configured to satisfy a condition of ${6 < \frac{\beta_{II}}{\beta_{T}} < 20},$  wherein β_(II) denotes a magnification of the first optical system and β_(T) denotes a magnification of the projection optical system.
 19. A projection optical system according to claim 18, further comprising a catadioptric illumination relay lens and a spatial light modulator (SLM) positioned to receive light from the catadioptric illumination relay lens and reflect said light towards the first and second optical systems.
 20. A projection optical system according to claim 18, wherein said projection optical system is configured to satisfy a condition ${4 < \frac{\beta_{I}}{\beta_{T}} < 30},$ wherein β_(I) denotes a magnification of the second optical system.
 21. A projection optical system according to claim 20, wherein said projection optical system is configured to satisfy a condition of |β_(II)|<|β_(I)|.
 22. A projection optical system according to claim 18, characterized, in operation with light having a central wavelength of about 193.3 nm and a spectral bandwidth of about 1 picometer, a first Strehl ratio at the central wavelength and a second Strehl ratio across the spectral bandwidth, both the first and second Strehl ratios exceeding 0.95. 